Classical fields problem

1) In classical electrodynamics, does a charged particle experience any force exerted by the electromagnetic field it creates itself?

2) In general relativity, does the world-line of a lonely point mass obey the spacetime curvature created by the stress energy tensor created by the point mass?

3) In general relativity, in a system of 2 point masses, does the world-line of point mass A obey the spacetime curvature created by the stress energy tensor created by A or does the world-line of point mass A obey the spacetime curvature created by the stress energy tensor created by both particle A and particle B?

4) In a gas of N particles of point masses, does all the world-lines of all the point masses obey the spacetime curvature created by the stress energy tensor created by the N point masses or N-1 point masses?

1) In CEM, a charged particle does experience a force due to its own EM field if it is accelerating, but the calculation of this force is still unsolved due to infinite behavior at the location of the charge and other conceptual difficulties.

2) There is no solution to Einstein's equation for a point-particle stress-energy tensor. So such a particle cannot even exist. Only extended bodies or black hole-type objects are allowed in general relativity. Reasonably-speaking, this same restriction should be made for every classical field theory. Doing so solves many problems, including Meir's claim that there are conceptual difficulties in flat-spacetime EM.

In general, objects always respond to the physically-measurable field. They don't know the difference between what they've produced versus what has been produced by other sources. Still, it's well-known that in many approximations, the self-field does not contribute to the motion. It never contributes if Newton's 3rd law were exactly true. But of course it isn't in relativistic field theories, so you get nonzero self-forces in extreme situations.

Can you give a reference to a textbook or a paper showing explicitly an example of such an effect? I would be interested in seeing this.

That depends on the level you want to see it at (and your background). The last chapter of Jackson talks about this a bit. Here's a quick writeup intended to teach the Lorentz-Dirac equation, which is the name of the equation that a charged "point particle" should satisfy: http://arxiv.org/abs/gr-qc/9912045.

I much prefer the viewpoint that classical charges are fundamentally extended objects, but deriving the equations of motion correctly is then much more complicated. There exist relevant references, but they're not easy to read.